Various strategies are available for producing and administering engineered cells for adoptive therapy. For example, strategies are available for engineering immune cells expressing genetically engineered antigen receptors, such as CARs, and for suppression or repression of gene expression in the cells. Improved strategies are needed, for example, to provide a wider range of target antigens and diseases that may be treated using such cells, to improve specificity or selectivity of the cells, e.g., to avoid off-target effects, and to improve efficacy of the cells, for example, by avoiding suppression of effector functions and improving the activity and/or survival of the cells upon administration to subjects. Provided are methods, cells, compositions, kits, and systems that meet such needs.